Elements of Distribution Theory [Paperback]

This introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics and researchers using statistical methods.Distribution theory consists of those areas of probability theory that are useful in understanding the development of statistical methodology, with the focus on the calculation and approximation of probabilities and moments. This detailed introduction uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, orthogonal polynomials, and saddlepoint approximations.Distribution theory consists of those areas of probability theory that are useful in understanding the development of statistical methodology, with the focus on the calculation and approximation of probabilities and moments. This detailed introduction uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, orthogonal polynomials, and saddlepoint approximations.This detailed introduction to distribution theory is designed as a text for the probability portion of the first year statistical theory sequence for Master's and PhD students in statistics, biostatistics, and econometrics. The text uses no measure theory, requiring only a background in calculus and linear algebra. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, converglCÏ